We could also obtain the result using the procedure NLMIXED. NLMIXED can solve a nonlinear least squares problem. Still, I really like NLP for this rather than NLMIXED or PROC MODEL. It is just a matter of knowing what the procedure is doing well enough to properly specify the convergence criteria.

Dale

--- Ban Cheah <BanCheah@WESTAT.COM> wrote:

> Interestingly PROC MODEL returns 418 for Dale's example. > > -----Original Message----- > From: owner-sas-l@listserv.uga.edu > [mailto:owner-sas-l@listserv.uga.edu] > On Behalf Of Dale McLerran > Sent: Thursday, April 13, 2006 2:24 PM > To: SAS-L@LISTSERV.UGA.EDU > Subject: Re: newton-rapson method > > > --- lisiqi77@YAHOO.COM wrote: > > > Hi, Dale, > > > > I really appreciate your comment--clear and helpful. But about the > > last comment on the convergence criterion, I am puzzled why this > would > > > be a > > problem. I choose this value (0.005) since several other similar > > studies used it too. I constructed a dataset (where I know R is > 0.12) > > like the following: > > > > data sample; > > input B B1 B2 B3 ROE1 ROE2 ROE3 P; > > datalines; > > 20 30 40 50 0.20 0.30 0.40 120.89 > > 21 31 41 51 0.21 0.31 0.41 127.96 > > 22 32 42 52 0.22 0.32 0.42 135.19 > > ; > > proc print; > > run; > > > > The least square method works perfectly, but min ABS(P - g(R)) > gives > > something like (although it did give me correct R value): > > > > WARNING: Your program statements cannot be executed completely. > > NOTE: ABSCONV convergence criterion satisfied. > > NOTE: At least one element of the (projected) gradient is greater > than > > 1e-3. > > WARNING: In a total of 1 calls an error occurred during execution > of > > the program statements. > > NLP attempted to recover by using a shorter step size. > > > > > > So is this the convergence criterion problem you are worried about? > > > > > > Thanks! > > Tracy > > > > Hi Tracy, > > I did kind of leave that hanging. I'm not sure that this post > will provide complete enlightenment of my thoughts, but hopefully > it will point out the problems that need to be considered. If you > minimize ABS(P - f(R)), then your convergence criterion may be > adequate. However, if you use least squares, then you may need > more stringent convergence criterion. > > I don't have time for much discussion right now, but take a look > at the following example. Note that when I first constructed a > test set, I had large ROE1-ROE3 and small B1-B3, just the > opposite of what you show. My choice of parameters does demonstrate > the need for stricter convergence criteria. > > /* Generate P from specified R, ROE1-ROE3, B, and B1-B3 */ > data test; > b=8; > roe1 = 600; > b1=0.7; > roe2 = 300; > b2=1.3; > roe3 = 200; > b3 = 0.25; > r = 418; > > P = B + (ROE1-R)*B1/(1+R) + > (ROE2-R)*B2/((1+R)**2) + > (ROE3-R)*B3/(R*((1+R)**2)); > output; > drop r; > run; > > > /* Invoke NLP to solve for R using LSQ criterion. */ > /* Convergence criterion is ABSXCONV=0.005. Note */ > /* that NLP indicates convergence meeting */ > /* ABSGCONV criterion but finds R=417.41. */ > proc nlp data=test absxconv=0.005 ; > bounds R >= 0; > lsq f; > decvar r=1; > f = (P -( B + (ROE1-R)*B1/(1+R) + > (ROE2-R)*B2/(1+R)**2 + > (ROE3-R)*B3/(R*(1+R)**2))); > run; > > > /* Invoke NLP again, but specify more stringent */ > /* criterion for gradient convergence. */ > proc nlp data=test absxconv=0.005 absgconv=1E-8; > bounds R >= 0; > lsq f; > decvar r=1; > f = (P -( B + (ROE1-R)*B1/(1+R) + > (ROE2-R)*B2/(1+R)**2 + > (ROE3-R)*B3/(R*(1+R)**2))); > run; > > > I don't pretend to know what represents optimal values for the > convergence criteria. However, if you want ABS(P - f(R)) within > 0.005 (which means [P - f(R)]^2<0.000025 when using LSQ objective > function), NLP may terminate due to some other criterion before > you meet the criterion that you specifically state. > > Hope this helps clarify the problem. > > Dale > > > --------------------------------------- > Dale McLerran > Fred Hutchinson Cancer Research Center > mailto: dmclerra@NO_SPAMfhcrc.org > Ph: (206) 667-2926 > Fax: (206) 667-5977 > --------------------------------------- > > __________________________________________________ > Do You Yahoo!? > Tired of spam? Yahoo! Mail has the best spam protection around > http://mail.yahoo.com >

--------------------------------------- Dale McLerran Fred Hutchinson Cancer Research Center mailto: dmclerra@NO_SPAMfhcrc.org Ph: (206) 667-2926 Fax: (206) 667-5977 ---------------------------------------

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